Logarithmic amplifier



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ATTORNEY Patented Feb. 7, 1950 LOGARITHMIC AMPLIFIER John A. Hipple, Jr., Verona, Pa., assignor to Westinghouse Electric Corporation, East Pittsburgh, Pa... a corporation of Pennsylvania,

Original application April 27, 1944, Serial No. 533,093. Divided and this application October 22. 1946, Serial'No. 704,853

2 Claims.

My invention relates to electrical networks, and in particular comprises an electrical network adapted to produce a quantity which varies in accordance with the logarithm of another quantity. These quantities may in a particular instance be electrical voltages or currents and in such cases the one may be of amplified magnitude in comparison with the other.

This application is a division of m copending application, Serial No. 533,093, filed April 2'7, 1944, for Electrical networks, now United States Patent 2,451,950, issued October 19, 1948.

For certain types of electric measurement, it is desirable to obtain an electric current which varies in proportion to the logarithm of another electric current. This is particularly true in the case of measuring instruments which must record wide variations of an electrical current or voltage, and must have scales which indicate the quantities with something like the same percentage precision when they are small that it does when they are large; in short where the instrument must have an expanded scale in recording the lower values of the quantities and a contracted scale in recording their higher values. Instruments employing so-called logarithmic charts are examples of such devices.

It is accordingly, one object of my invention to provide an electrical network having an output current which has a substantially accurate logarithmic relation to an input current.

Another object of my invention is to provide an electrical network in which an output current of substantia1 magnitude bears an exponential relationship to an input current.

It is still another object of my invention to provide an arrangement in which the mechanical displacements of a recording arm bear an exponential relationship to the magnitude of an input current.

It is still another object of my invention to produce an arrangement in which the mechanical displacements of one member are proportional to the logarithm of the mechanical displacements of another member.

It is a still further object of my invention to provide an arrangement in which movements of a recording member are adapted to accurately record on logarithmic charts the values of a control quantity.

Still another object of my invention is to provide an electrical network in which the output voltage is proportional to the exponential of th input voltage.

It isstill another. object of my invention; to

2 provide an electrical network in which the output voltage is proportional to the logarithm of an input voltage.

Other objects of my invention will become apparent upon reading the following description taken in connection with the drawings, in which:

Figure 1 is a schematic diagram of an electrical network embodying the principles of my invention to produce an output voltage proportional to the exponential of the input voltage; and

Fig. 2 is a schematic diagram of an arrangement in which the output voltage is proportional to the logarithm of the input voltage.

Referring in detail to the drawing, an electrical generator I, which may be of the electron tube type well-known in the art, produces electrical pulses of short duration compared with the time interval separating them, these pulses and the intervals separating them may, for example, be represented by the wave form 2 shown within the confines of the rectangle l in the drawing. Electrical generators of this type are well known in the art and require no detailed description here. The output wave of the form just described is impressed on a primary winding 3 having a secondary winding 4 connected through a suitable bias battery 5 to impress voltage on the control electrode of an electron tube 6 which is preferably of the gaseous discharge type well known in the electronics art. Between the anode and the cathode of the tube 6 are connected a capacitor 1 and in parallel therewith a resistor 8 and a constant voltage source 9.

The output of the pulse generator I is likewise connected to control the output of a saw-tooth wave generator H of a type too well known in the electronics art to require detailed description, the saw-tooth generator producing discharges having the same period as the voltage pulses of the pulse generator I, and the steep portion of the saw-tooth wave being synchronized in time with the aforesaid pulses. The output of the saw-tooth generator II is shunted through a suitable resistor I2 having one end grounded. The saw-tooth generator II should be so poled as to make its ungrounded end positive when at the positive maximum of the wave. An electron tube l3 which is preferably of the high vacuum type has its anode connected to the positive terminal of a suitable source Bl of unidirectional voltage, the negative terminal of said source being connected to the cathode of tube l3 through an output resistor l4. Between the con.- trol electrode and the ungrounded end of the resistor l2. are serially connected a variable. source ijnegative terminal of the voltage source 9.

[6 of bias potential and a pair of terminals l'!-|8 for the electrical quantity which is to be recorded. The voltage to be impressed across terminals ll, l8 which might be the output of a direct-current amplifier should have its negative terminal adjacent bias source it and its positive terminal adjacent the grid of tube I3. As one example of the latter, this quantity may be the voltage drop picked olf from a potentiometer I8A by a movable contact (8B which is mechanically displaced in proportion to a current or other quantit to be measured. For example, the movable contact may be carried by the recording arm of a recording ammeter or voltmeter of standard type commonly sold on the open market.

The terminals of the cathode resistor M are connected through a suitable bias battery H! between the control electrode and the cathode of a gaseous discharge electrical discharge tube 2| which may, for example, be a thyratron tube of :a type commonly soldon the open market. The anode and cathode of the discharge tube 21 shunted by a. capacitor 21A are connected in series with a suitable voltage source 22 through the primary winding 23 of a transformer, of which the secondary winding 24 is connected through a suitable bias battery 25 and two equal resistors 26 and 2.6A-to impress a voltage between the control electrode and cathode of an electron tube 21 which is preferably of the high vacuum type. The anode of the tube 2'! is connected to the cathode of the tube 6 while its cathode is connected through :a primary winding 28 to .the A capacitor 29 is connected through a rectifier .30 "to a secondary winding cooperating with wind- ;ing 28 and is shunted by a resistor 3 l.

The mode of operation of the network just described will now be explained. The value .of

the bias battery is adjusted so that in the in- ,terval between pulses of the pulse generator I,, the tube 6 is nonoonductive. The value of the :bias battery .25 is likewise adjusted so that when no voltage is impressed by the secondary wind- :ing 24, "the electron tube 27! is non-conductive. :Under such circumstances, the capacitor 1 will 'be charged through the resistor 8 .to substantially the voltage of the source 9. When there- :after the pulse generator 1 .impresses a voltage pulse on the control grid of the tube 6 through .the transformer windings 3 and A, the capacitor 'I will quickly discharge through the tube 6, then extinguish .tube :5 and begin to recharge from .source :9 through resistor 8. The voltage e across the terminals of the resistor 8 will then vary 7 exponentially with the time so that it will be represented by the equation t (1) e=Ee RC where E is the voltage of source 9, R the resistance of resistor 8, C is the distributed capaci tance of the charging circuit of capacitor 7 and the time during which charging proceeds, and e the base of natural logarithms. At the same time that the voltage pulses from generator SI starts-the discharge of the capacitor 1 it initiates a saw-tooth wave of the generator H and the voltage of the latter will increase at a uniform rate with time. The value of the bias source iii is so adjusted that with the minimum :voltage which is .to be measured impressed across the terminals l1--il:8, the current flowing through resistor 174 from tube 13 is just sufficient when sthesaw-tooth voltageof generator H reaches its 4 peak to cause the gaseous discharge tube 2| to conduct substantial current. Under this condition an entire period of the saw-tooth wave elapses between the initiation of charging of capacitor '1 and the energizing of tube 21. In other words, the "voltage drop 2 across winding 28 is represented by Equation 1 if t therein is taken equal to the period of pulse generator i.

If now the voltage impressed on the terminals l1|8 is made larger, the voltage drop across the resistor 14 will reach the critical value capable of causing a discharge to start in the tube 21 .at an earlier point in the cycle of the saw-tooth generator -II and will produce a pulse of voltage rendering the tube 2:! conductive similarly at an earlier'time in'the cycle of the saw-tooth gen- .erator vi 1'. In fact the relationship between the voltage e, impressed on terminals l1, l8 and the time ,tpin the cycle of the saw-tooth wave is expressed by the equation (2) t rm-o Therefore, the voltage which will be suddenly impressed upon the winding 28 will be proportional to the exponential of the time. We can however by substituting the value of t from Equation 2 in Equation 3 express :e in terms of e1 thus e=E e EE e e (E 5.

The tube 21 remains conductive only for the short duration .of the pulse impressed on its control electrode 'by the secondary winding 24, so that only a pulse of current flows through winding 28. During that pulse, -the'l capacitor .29 charges substantially through rectifier 30 .to a voltage equal to the :potential drop across wind- ?ing 28; but it is able to feedtacurrent substantially proportional to this voltage to which it is charged through a .load circuit such .as resistor :31 to which it is connected in shunt. iSuc'h a load circuit may, for example, comprise the recording element of a recording voltmeter or might be the input circuit of a power amplifier. The deflections of this recording element, being proportional to the average value during the period betweensuccessive pulses of the generator :I of the exponential voltage across winding 28, are like the latter represented by Equation 4. The recording .element is,'.1accordingly, adapted to record varying values of the voltage across input terminals H- l8'on a; chart having an exponential current or voltage scale.

Equation 4 may be transposed to read .116 KRC 6 .1

1. a a logage es of the exponential amplifier 44.

minals I I -l8 is thus seen to be'proportion'al'to the logarithm of the voltage e impressed across resistor 3|, it will be noted that the voltage e1 across terminals |'||8 is the input voltage of the network while that across resistor 3| is the output voltage. We have thus an arrangement in which the input voltage is proportional to the logarithm of the output voltage; but for many purposes it is desirable to obtain an electrical network in which it is the output voltage which is proportional to the logarithm of the input voltage. An arrangement which caused a voltage across the terminals |'||8 to automatically vary until the voltage across the resistor 3| was equal to a voltage impressed on a pair of input terminals would clearly efiect the above-mentioned desired result. This may be accomplished either mechanically or electrically by recorders now marketed; for example by the Leeds & Northrup Speedowax or Microwax. In Fig. 2 I show a circuit arrangement in which the network shown in Fig. 1 may be embodied to produce this desired result.

1 Referring to Fig 2, 4| is an ordinary amplifier in' which the output voltage is linearly proportional to the input voltage; that is to say, it is equal to A times the input voltage. In multiple with the output terminals of the amplifier 4| are connected the input terminals 4243 of an exponential amplifier of the type shown in Fig. 1; that is to say the terminals 42-43 of exponential amplifier 44 correspond to the input terminals 8 in Fig. l. A linear feedback circuit which may be a second amplifier in which the output voltage is proportional to B times the input voltage has its input terminals 46-41 likewise connected in multiple with the output terminals of the amplifier 4|. The amplifiers 44 and 45 are connected to the input terminals 4B49 of the system in such a way that amplifier 44, opposes the input voltage as in acting on the input of the linear amplifier 4| while amplifier 45 assists it.

Disregar-ding for the moment the voltage impressed on the input circuit of linear amplifier 45, the net voltage impressed on the input terminals of amplifier 4| is equal to the input voltage as on terminals 48-49 minus the output volt- .Since the output voltage c4 of amplifier 4| is impressed on terminals 42-43 of the exponential amplifier 44, the value of ea the output voltage of the latter is shown by Equation 4 to be e =E c Since the output voltage a; of the amplifier 4| is A times its input voltage, the following equation may be written:

By merely transposing, Equation 6 may be rewritten to read:

and by taking the logarithm of each side this in turn becomes:

It is thus evident that by making the quantity 1 e log,

A, i. e., the amplification of amplifier 4| large enough an arrangement comprising simply the linear amplifier 4| with the exponential amplifier 44 arranged as a feedback circuit for the latter will produce an output voltage e4 which is approximately proportional to the logarithm of the input voltage e2, except at very small values of the latter.

- However, the employment of the feedback circuit 45 in Fig. 2 makes it possible to avoid even the discrepancy involved in this approximation and to make the output voltage 64 exactly equal to the logarithm of the input voltage to the terminals 48-49.

When we add a term to the Equation 6 to take care of the circuit 45, we obtain the following:

It is obvious that if the quantity showing that we have a network in which the output voltage is strictly proportional to the logarithm of the input voltage to terminals 48-49.

To obtain an output voltage strictly proportional to the logarithm of the input voltage the should exist; i. e., the gain of amplifier 45 should thus be inversel proportional to that of amplirelationship The arrangement described in Fig. 1 has been shown to produce an output voltage across resistor 3| which is related to the input voltage across terminals 11, [8 by Equation 4 which involves an exponential e 1 having a positive exponent. However, by a comparativel simple change, it is possible to alter the system into one in which the voltage across resistor 3| will be an exponential having a negative exponent. This alteration consists merely in reversing the polarity of the potential applied to the terminals When this is done, we have, instead of Equation 2, the relationship (14) e1=Kt Substitution of this relationship in Equation 3 gives (15) e=Ee Under such circumstances, it will be noted that when the voltage impressed upon terminals ||--|8 is of a. comparatively small value, the time during which capacitor 1 has charged before its voltage is impressed across output winding 28 is short, and the charging current flowing through resistor 8 is comparatively large, giving a relatively wide-scale deflection to a recording element connected across capacitor 29. On, the

arcane 7 other hand; it the voltage: impressed, across terminals iL-tB. is. large, the time during which capacitor 1 has beenv charging before tube 2'! becomes conductive will be large and the charging a current through winding 28' will be correspond- 17 a: E KRC log, %EKRC log, E 18 a: KRC log, 25 K120 log, 5

Thus, the Fig. 2 arrangement has been transformed into one in which the voltage e4 across the output terminals is proportional to the logarithm of the inverse of the input voltage.

It will be noted that the logarithmic relationship of the apparatus above described is dependehtv only upon the correlated action of a constant voltage. source 9, an ohmic resistance 8 and a capacitor 1 and does not depend upon such quantitles as the characteristic curves of electron tubes. The elements 9, 8 and l are all elements which can be readily made to have constant and invariable operating characteristics little afiected by either ageing, operating or environment temperatures. As a result, the above described arrangement has been found to produce and, maintain a constant logarithmic relationship between For example, I 45 its input and output voltages. have operated such an arrangement as appears in 8 Fig 1 to record currents varying o r 3 mm of 1000 to 1 and found the constants of the logarith-mic recording scale to vary by less than .2 of a percent over a half hour period.

While I have described a particular embodiment of my invention to comply with the requirements of the patent statutes, other embodiments and uses of that principle exist and will be selfevident to those skilledin the art.

I claim as my invention:

1. In combination, a linear amplifier having its output terminals connected in multiple with the input terminals of a second linear amplifierand also with the input terminals of an ampli i her in which the output voltage is proportional to the exponential of its input voltage, and:

means for impressing on the input. terminals of the first-mentioned amplifier a voltage equal to a desired input voltage minus the sum of the output voltages of said second amplifier and said third amplifier.

2. In combination, a linear amplifier having an output voltage which is A times its input voltage having its output terminals connected in multiple with the input terminals of a second: linear amplifier having an output voltage which is B times its input voltage and also with the input terminals of an amplifier in which the out-- put voltage is proportional to the exponential of its input voltage, and means for impressing on the input terminals of the first-mentionedamplifier a voltage equal. to a desired input voltage minus the sum of the output voltages of said sec ond amplifier and said third amplifier, B being equal to 1 divided by A.

JOHN A. HIPPLE, JR.

REFERENCES CITED The following references are of record in the Name Date Martin June 3, 1941.

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